Hydrogen-bond geometry and its isotope effect in crystals with OHO bonds—revisited

Journal of Molecular Structure 552 (2000) 63±70

www.elsevier.nl/locate/molstruc

Hydrogen-bond geometry and its isotope effect in crystals with OHO bondsÐrevisited M. Ichikawa* Division of Physics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan Received 20 October 1999; received in revised form 5 January 2000; accepted 5 January 2000

Abstract The O±H vs O´ ´´O correlation in OHO hydrogen bonds is brie¯y reviewed based on the development during these twenty years and the geometric isotope effect DR is revised including the new data. It is pointed out that the following still remains to be settled: (1) whether or not the O±H distances in asymmetric bonds for the same O´ ´´O distance scatter in short hydrogen bonds at low temperature; (2) whether there exists or not the exceptional compounds that exhibit the extraordinarily large geometric Ê ); (3) where the critical hydrogen-bond distance is located; and (4) the peculiar hydrogen-bond geometry isotope effect (,0.1 A and its origin in high-pressure ice. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Hydrogen-bond geometry; Geometric isotope effect; Critical hydrogen-bond distance; High-pressure ice

1. Introduction Since the work by Nakamoto, Margoshes and Rundle in 1955, it is well known that in X±H´ ´ ´Y hydrogen bonds, the X±H bond is lengthened and the lengthening increases with decreasing X´ ´´Y and H´ ´ ´Y distances. Many authors since then have been involved in compiling and revising these correlations (e.g. Refs. [1±3]). The rich accumulation of the data during the seventies has been achieved by Olovsson and JoÈnsson [4] and successively by the present author [5]. Further enrichment of the data, especially in short and very short region and the investigation of the empirical relation have been continued [6±8]. As for the isotope effect in the hydrogen-bond parameters, such as the hydrogen bond distance X´ ´ ´Y and the * Tel.: 1 81-11-706-4416; fax: 1 81-11-717-4926. E-mail address: [email protected] (M. Ichikawa).

two proton site separation H´ ´ ´H, a laborious compilation has been done by Sokolov et al. [7] during the eighties since earlier work [4,5]. Among various types of hydrogen bonds, the largest quantity of the data is available in the OHO hydrogen-bond system. Owing to these circumstances, the description will be con®ned to OHO bond in this paper. The studies on the O±H vs O´ ´´O correlation are reviewed based on the development during these 20 years and the geometric isotope effect (or Ubbelohde effect) DR, the isotope effect in O´ ´´O distance, are revisited including the recent new data. The purpose of this paper is to review some of recent work and to comment on the points still to be investigated and settled. The terminology used is followed to the preceding papers [4,5] as below. The term ªsymmetricº is widely used in two different meanings: one is referred to the symmetry of the proton potential shape and the other is to the centered position of the proton (for details see Ref. [5]). In this

0022-2860/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0022-286 0(00)00465-8

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M. Ichikawa / Journal of Molecular Structure 552 (2000) 63±70

Joswig et al. [6] examined this O±H vs O´ ´´O correlation in asymmetric bonds, by adding 25 neutron diffraction determinations of very short hydrogen bonds. They stated that 1. most of the O±H distances are on the lower side of the smooth curve by Ichikawa [5]; and 2. the dispersion of points is too large to justify the elaborate course of the smoothed curve by Ichikawa [5] (see Fig. 1). Fig. 1. Correlation between O±H and O´´´O distances in OHO bonds, taken from Ref. [6]. The smoothed curve and dots from Ref. [5]; crosses from Ref. [6].

paper the term ªsymmetricº is used in the former sense, i.e. with respect to the crystallographic equivalence of the donor and the acceptor atoms averaged in space and time. The term ªsingle minimumº or ªcenteredº are also used if necessary to describe the situation more properly. In discussion of ice under high pressure, however, the term ªsymmetricº will be used in the latter sense, following common usage.

2. O±H vs O´ ´ ´O correlation In the O±H vs O´ ´ ´O correlation diagram for asymmetric bonds, a considerable spread of the O±H distances is seen for the same O´ ´ ´O distance in the very short hydrogen-bond region, presumably re¯ecting the skew and ¯atness of the proton potential. There has been a question of the average curve in the correlation diagram (e.g. Ref. [3]). In the O±H vs O´ ´´O correlation diagram given by Olovsson and JoÈnsson [4], the hyperbola-like smoothed curve for asymmetric bond is seen. In successive compilation done by the present author [5] a smoothed curve was drawn (Fig. 1) and used to derive the other quantities. This smoothed curve had the following characteristics: 1. it asymptotically approaches to the centered proton straight line at the shortest limit of O´ ´ ´O distance Ê ; and around 2.40 A Ê. 2. it has an in¯ection point at around 2.45 A

Based on these results, they concluded that the O±H length is de®nitely a function not only of O´ ´´O, but also of other causes, which become more important with the weakening of O±H. This scatter of the data points seems to indicate that the environmental effect manifest itself in the O±H Ê where the O±H length in the region less than 2.5 A and H´ ´ ´O distances are close to each other. This environmental effect is speci®c in each crystal and arises from the chemical asymmetry outside the O± H´ ´ ´O system. On the other hand, it is well known that the environmental effect appears in O±H´ ´´O angles for long bonds. More recently, Steiner and Saenger [8] reexamined the O±H vs O´ ´ ´O correlation in asymmetric bonds from high-resolution low-temperature neutron-diffraction determinations of organic molecules. They pointed out that the abovementioned earlier works [5,6] are based on the data measured at room temperature and this results in relatively large errors, primarily due to thermal smearing of the H-atom position. They stated that 1. the restriction to low-temperature data considerably reduces the scatter of data points with earlier studies of the same relations [4,6]; 2. the dependence of O±H on O´ ´ ´O is perfectly smooth, and there is no indication of sudden changes of the slope or even of in¯ection points that were reported based on the lower quality [5,6]. It seems well established through the studies so far accumulated [4±6,8,9] that the shortest limit of OHO Ê . However, it still seems unclear bonds is around 2.4 A whether the scatter of the O±H distance appears or not in short hydrogen bonds at low temperature.

M. Ichikawa / Journal of Molecular Structure 552 (2000) 63±70 Table 1 Compound names and literature used (a) Fig. 2

Reference

KH2PO4 KH2AsO4 RbH2PO4 CsH2PO4 (NH4)3H(SO4)2 (NH4)4H2(SeO4)3 H2SO4´4H2O H2SQ KH3(SeO3)2 NaH3(SeO3)2 LiH3(SeO3)2 NaHSeO3 (NH4)2H3IO6 YH(C2O4)2.3H2O KHCO3 (COOH)2´2H2O LiHC2O4´H2O N2H5HC2O4 (H5O2) 12SO422 NaHC2O4´H2O KH(CF3COO)2 [Ni(AO)2-H]Cl´H2O QNA-H [ImH] 1[HMal] 2 2´Et2´HZnCl3 C6H3(COOH)(OH) ´SO3H´2H2O KHO(CHCCOO)2

H&D [18] H&D [34] H&D [35] [36] H [19] H [38] H&D [40] H&D [41] H [42] H&D [44] H [12,14] H [10] H&D [45] H&D [46] H&D [47] H&D [48] H&D [15] H&D [49] H&D [50] H&D [41] H&D [51] H&D [52] H [54] H [56] H&D [58] H&D [59] H&D [60]

(b) Fig. 3 KH2PO4 RbH2PO4 CsD2AsO4 PbHPO4 NH4HSeO4 RbHSeO4 H2SQ KH3(SeO3)2 CsH3(SeO3)2 NaH3(SeO3)2 (NH4)2H3IO6 Na2CO3´NaHCO3´2H2O KH(CHCl2COO)2

Reference

D [37] D [39] D [43] D [13,14] D [11]

D [55] D [57]

H&D [61] H [18] H [35,36,62] H [63,64] H [65] H [66] H [67] H [44] H [68] H [12] H&D [46] H [69] H [53]

D [16,18] D [35,36] D [70] D [64]

65

compilation by Sokolov, Vener and Savel'ev. The same criterion as that in Ref. [5] was taken for adoption of the data: the data with the e.s.d.s equal to or Ê in O´ ´ ´O for both protonated and smaller than 0.010 A deuterated compounds are taken. (The data for bis(3-amino-3-methyl-2-butanone oximato)nickel(II) chloride monohydrate are not included for the reason as stated in Ref. [7].) Consequently, The present compilation includes 52 symmetric and asymmetric hydrogen bonds from 30 compounds (Table 1(a) and Fig. 2). As a whole, the more the data are accumulated, the more the correlation seems to smear, compared to the earlier compilations [4,5]. The reason of the smearing of the correlation may be at least partly due to the interaction among more than two hydrogen bonds in crystals which constraints individual isotope effect [5]. However, the basic characteristics are still valid, i.e. 1. the magnitude of the geometric isotope effect is Ê ; and con®ned within 0.03 A 2. an expansion is only seen between around 2.43 and Ê. 2.65 A There are, however, three exceptional data points at Ê : 0.044 A Ê in LiH3(SeO3)2 [10,11] and around 2.6 A Ê in NaH3(SeO3)2 [12,13]. It is 0.037 and 0.040 A pointed out that these compounds are common in having H2SeO3 and HSeO3 ions. It might be probable that the true isotope effect is not realized due to the geometrical restrictions of the hydrogen-bond network in these crystals with SeO3 ions similar to the cases discussed earlier [5]. However, since in Na Ê ) [14] is NaH3(SeO3)2 the smaller magnitude (0.013 A reported in the other literature, it may be premature to conclude the origin of a large isotope effect. As for Ê from a-(COOH)2´3H2O two data points near 2.9 A [15] the deviations from correlation were already interpreted due to direct coupling among hydrogen bonds.

3. Geometric isotope effect

4. Discussion

As far as the author is aware, the only laborious compilation of the geometric isotope effect is that by Sokolov et al. [7] since that by Olovsson and JoÈnsson [4] and by the present author [5]. Therefore, inclusion of the new data was tried in addition to

4.1. Critical hydrogen-bond distance in symmetric bonds Associated with structural phase transition, one of the central issues in hydrogen-bond distance is the

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M. Ichikawa / Journal of Molecular Structure 552 (2000) 63±70

Fig. 2. The geometric isotope effect DR; …O¼O†D 2 …O¼O†H ; as a function of the hydrogen-bond distance (O´´´O)H.

critical hydrogen-bond distance Rc in symmetric bonds, where the proton occupation changes from two equidistant sites with respect to symmetry element to one site at the center of the hydrogen bond. In our previous paper [5], it was assumed that the proton sites in symmetric bonds can be expressed as the superposition of proton position of two asymmetric bonds with the same O´ ´ ´O distance. Then, the smoothed curve for asymmetric bonds was used to estimate the separation between two proton sites and other quantities. It was only due to the lack of the directly measured data. However, based on the recent studies as described above, this may not be correct for very short hydrogen bonds. Since the oxygen atom with shorter distance to the proton in an OHO system is recognized as the donor (and the other is the acceptor), the data points of O±H distance never exceed the centered proton line with O± H ˆ (O´ ´ ´O)/2 and asymptotically approach to it. However, as discussed by Nelmes (e.g. Ref. [16]), in actual symmetric bonds the discontinuous change from the disordered two-site proton to the centered proton will occur, when the amplitude of thermal vibration along the bond reaches to the top of the potential barrier with decreasing O´ ´´O distance, i. e. p u ˆ d=2 where u is the mean square amplitude along the bond and d the two-site proton separation. The proton will then lose two-site character discontinuously before reaching the shortest distance. The

critical proton two-site separation d c was estimated Ê [16]. This means that a certain gap with as ,0.2 A Ê should exist in the O±H vs O´ ´´O correlation ,0.1 A for symmetric bonds. In this meaning it may not be correct to assume the proton sites in symmetric bonds as the superposition of the proton position of two asymmetric bonds. Directly measured values of d in symmetric bonds are much less than those in asymmetric bonds. In Fig. 3 the proton (or deuteron) two-site separation d H (or d D), H´ ´´H (or D´ ´ ´D), directly measured from neutron diffraction are shown against (O´ ´´O)H (or (O´ ´´O)D). (More exactly, we should denote them as the d values in symmetric bonds that could be successfully analyzed with the two-site model.) This includes 20 hydrogen bonds from 12 compounds and 10 deuterium bonds from 5 compounds (Table 1(b)). These data also include 5 data under high pressure (3 hydrogen and 2 deuterium bonds). As far as the present data are concerned, no obvious differences are seen between hydrogen and deuterium bonds, and between ambient pressure and high pressure. As seen from Fig. 3, the data given are compatible with Ê to 0 at that there is a discontinuous change from 0.2 A Ê around 2.45 A. Unfortunately, it is dif®cult to determine the critical bond distance from diffraction experiment, since it is known that the observed proton density is equally interpreted either by two-site proton model or

M. Ichikawa / Journal of Molecular Structure 552 (2000) 63±70

67

Fig. 3. The two proton site separation d H (or d D), H´´´H (or D´´´D), as a function of the hydrogen-bond distance (O´´´O)H.

centered proton model for very short bonds [1]. Instead, let us try to estimate the critical hydrogenbond distance from other viewpoint. We assume that every hydrogen bond has the common critical bond distance. Then, ®rst, as the evidence for the upper limit of two-site proton we can use the fact of two resolved proton density peaks from a high-resolution neutron diffraction study. The shortest distance with Ê in KH2PO4 two resolved proton peaks is 2.4829(4)A (KDP) at T c 1 2 K [17,18]. Second, the information can be derived from dielectric spectroscopic data, although it is indirect information. Among the compounds exhibiting Debye-type dielectric dispersion character, which is the evidence for order± disorder transition, the shortest O´ ´ ´O distance is Ê in CsH2PO4 (CDP) near Tc [19]. On the 2.470 A other hand, the longest distance with zero geometric  may be used as the isotope effect DR ˆ 0; 2:44A; lower limit [5]. Alternatively, we can use the isotopic ratio of the pstretching frequency n (OH). n…OH†=n…OD† < 2 in very short bonds may be regarded as the evidence of symmetric singleminimum proton potential, since the potential is expected to be of symmetric single-minimum type both for protonated and for deuterated bonds. The plongest distance keeping Ê [20]. Thus, if the n…OH†=n…OD† < 2 is 2.44 A above criteria are justi®ed, we can con®ne the Ê . It will be critical bond distance to 2.44±2.47 A

shown later that the case in ice under high pressure contradicts with this range of O´ ´´O distance. 4.2. HCrO2-type compounds The central issue of the geometric isotope effect remained is what is the maximum magnitude realized. As we have seen, the magnitude in most of the Ê except a compounds is con®ned to a range 0±0.03 A few compounds. There are, however, a group of materials, a-HCrO2, b-HCrO2 and a-HCoO2, which nominally exhibit an extraordinarily large expansion Ê ) of the hydrogen bond on deuteration. a(,0.1 A HCrO2 was the most studied among them. The magnitude of the geometric isotope effect in the HCrO2 Ê , depending system is in the range of 0.06(3)±0.10(2)A on the combination of the space group and the literature data adopted [21,22]. This would mean that the geometric isotope effect is 2±3 times larger than the maximum value commonly observed. However, judging from the combined standard deviations, it seems dif®cult to draw a de®nite conclusion. If the reported isotope effect is really true, the question is: why are HCrO2 and HCoO2 so exceptional? We notice some characteristic structural features in these systems (Fig. 4). Firstly, the OHO unit along the c-axis is located in a layer perpendicular to the c-axis and sandwiched by a Cr atom layer. In hydrogen-bonded crystals the observed expansion of

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M. Ichikawa / Journal of Molecular Structure 552 (2000) 63±70

4.3. Peculiar behavior of hydrogen-bond geometry in high-pressure ice

Fig. 4. Crystal structure of a-HCrO2 (space group R3Åm). The ®lled spheres: Cr atoms; the open larger spheres: O atoms; the open smaller spheres: H atoms. The Cr±O and O±H bonds are represented as sticks. The hexagonal unit cell is also shown.

the O´ ´ ´O distance is in general a result of a compromise with other effects in the environment surrounding the OHO system (like cation coordination polyhedra). The geometric isotope effect is thus smeared out or suppressed due to such a situation in the crystals. The separated layer structure of the aHCrO2 system seems to allow the hydrogen bond to expand without competing with other factors. Secondly, considering the hydrogen-bond network, the HCrO2 system is one of the simplest compounds with 0-dimensional hydrogen bond network (isolated H-bond system) [23±25]. Thus we may say that HCrO2 is a ultimate 0-D system. From these points of view, it seems very interesting to settle the magnitude of the geometric isotope effect in these crystals. Recently we have started a systematic study on the HCrO2 and DCrO2 systems [26].

The recent development of high-pressure experiments opened a new stage in the study of the hydrogen bond in ices under high pressure (phase VII, VIII and possibly X). Nelmes et al. [27] performed a neutron diffraction study of deuterated ice up to 10 GPa and got a small variation 0:4…4† £ 1023 A GPa21 for the pressure dependence of O±D distance. In the interpretation of the results, they ascribed the principal effect of pressure up to (at least) 10 GPa to reduce the D´ ´´O force constants without changing the O±D bond distance signi®cantly. Further, they considered that there is no reason to suppose that O±H and O´ ´ ´O in ice under pressure will be related in the same way as they are in an average O±H´ ´ ´O bond under varying chemical environments at constant (ambient) pressure. They suggested that below the O´ ´´O range Ê ), O±H distance increases studied (i.e. less than 2.7 A more rapidly with decreasing O´ ´´O than ambientpressure empirical relationship [27]. The same interpretation was introduced as well for the stretching frequency n (OH) vs O´ ´´O correlation. Besson et al. [28] stated that the experimental results, as well as calculation, contradict the belief widely spread in chemical physics that n (AH) frequency shifts are strongly correlated to lengthening of the A±H bond and that it is, therefore, not necessary to assign the decrease of the stretching frequencies in hydrogenbonded solids to an increase of the covalent hydrogen-bond length. In connection with the transition from phase VII or phase VIII to phase X with symmetric (centered) hydrogen bond, many authors tried to calculate or estimate the critical bond distance Rc. Schweizer and Ê Stillinger [29] derived Rc as 2.45, 2.46 and 2.505 A depending on the theoretical approach. Benoit et al. Ê (read from Fig. 2 [30] calculated Rc as around 2.365 A of Ref. [30]) from the ab initio path integral techÊ nique. The Rc value was estimated as 2.34±2.37 A Ê for deuterated ice [31] from for ice and 2.29±2.34 A Raman spectroscopic measurement under high presÊ from Raman scattering and X-ray sure or 2.32 A diffraction studies of high-pressure ice [32,33]. Both Rc values calculated theoretically and estimated Ê shorter than that derived experimentally are ,0.1 A empirically discussed above, except for the theoretical

M. Ichikawa / Journal of Molecular Structure 552 (2000) 63±70

ones during the eighties. This discrepancy is serious, if we take into account that the shape of the proton potential may change quite drastically for the change Ê in the range of short hydrogen bonds. of ,0.1 A Consequently, the peculiar behavior of hydrogen bonds in ice under pressure emerges. We have so far assumed implicitly or explicitly that the interrelation among O±H, H´ ´´O and O´ ´ ´O distances are determined principally within the O± H´ ´ ´O system and are modi®ed slightly by the in¯uence of chemical environment, and that an average empirical relation can be applied universally not only for a variety of compounds at ambient pressure, but also for a material under high pressure. If the n (OH) vs O´ ´´O and the O±H vs O´ ´ ´O correlation at ambient pressure is not valid for ice under pressure, it will then be interesting and important to elucidate its reason: What factor makes the difference in the hydrogen-bond character between various compounds at ambient pressure and ice under high pressure? 5. Concluding remarks The following emerged as the points to be further elucidated or settled from the earlier discussions. 1. The O±H vs O´ ´ ´O correlation for asymmetric bonds To settle whether the scatter of the O±H distance for the same O´ ´ ´O distance appears or not in short hydrogen bonds at low temperature 2. The geometric isotope effect To con®rm if there really exist exceptional compounds that exhibit the extraordinary large Ê) geometric isotope effect (,0.1 A 3. The critical hydrogen-bond distance To settle where the critical hydrogen-bond distance is located 4. Peculiar hydrogen-bond geometry in high-pressure ice To investigate further the O±H vs O´ ´ ´O correlation and the critical hydrogen bond distance and also its origin of the peculiarity. References [1] W.C. Hamilton, J.A. Ibers, Hydrogen Bonding in Solids.

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69

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